EARTH GEOMETRY
In this chapter you will learn how to:

understand and use the following geographical concepts: great and small circles, latitude
and longitude, the Equator and the Greenwich meridian

use latitude and longitude to locate positions on the Earth’s surface

calculate arc lengths of a circle

convert between nautical miles and kilometres

calculate distances between two points on the same great circle, in nautical miles and
kilometres

understand the meaning of a knot as a measure of speed and use it to solve problems

calculate time differences using differences in longitude

use standard time zones and the International Date Line to solve problems involving travel,
communication and daylight saving.
MODELLING THE EARTH
The following items are useful teaching and learning aids for understanding the Earth geometry
concepts introduced in this chapter: world globe, atlas, orange and knife to cut it with, tennis ball,
golf ball or basketball, black markers or rubber bands.
90°N
60°N
40°N
40°E
40°W 0°
180°
60°W
60°E
0°
Equator
40°S
60°S
90°S
LATITUDE AND LONGITUDE
When describing the location of a point on a number plane or map, we use a coordinate
system involving ordered pairs (x, y).
P has coordinates (3, 1) on this number plane.
Positions on the Earth’s surface also can be described by a coordinate system, one involving
latitude and longitude. However, because the Earth is a sphere, we must use a special grid
of lines that run across and down a sphere.
The diagrams below illustrate this grid on a world globe (3D) and flat world map (2D).
GREAT AND SMALL CIRCLES
The Earth is a sphere. If you cut any ‘slice’ through a sphere, the shape of the slice is a circle.
The circle can be of different sizes, ranging from very small (if you slice near the edge) to large
(if you slice through the centre of the sphere).
A slice that goes through the centre of a sphere is called a great circle, and its radius is the same
as that of the sphere.
Any other slice is called a small circle, because its radius is smaller than that of a great circle.
Small Circles
Great Circles
PARALLELS OF LATITUDE
Parallels of latitude are imaginary lines that run across and around the Earth. They are parallel
circles of differing sizes. The main parallel of latitude is the Equator, which is a great circle
labelled 0°. The other parallels of latitude are small circles either north or south of the Equator.
Half of a sphere is called a hemisphere, and the Equator divides the world into the northern and
southern hemispheres.
Northern hemisphere
75°N
60°N
45°N
30°N
15°N
0°
15°S
30°S
45°S
60°S
Southern hemisphere
Half of a sphere is called a hemisphere, and the Equator divides the world into the northern and
southern hemispheres. The angle of latitude is the angle that a line from the centre of the Earth,
O, to a parallel of latitude makes with the Equator. The diagram illustrates the 50°N parallel of
latitude.
90°N
50°N
Angle of Latitude
50°
O
Equator
90°S
0°
Parallels of latitude range from 90°N to 90°S. 90°N is the North Pole, 90°S is the South Pole.
Because they are the top and bottom ‘ends’ of the Earth, they are dots rather than circles.
MERIDIANS OF LONGITUDE
Meridians of longitude are imaginary lines that run down the Earth. They are great semicircles
between the North and South Poles, so they are not parallel but look like lines on the segments
(‘wedges’) of an orange.
The main meridian of longitude is called the Greenwich meridian or prime meridian. It is 0°
the longitude, and passes through the Royal Greenwich Observatory in London, UK. The other
meridians of longitude are either east or west of the Greenwich meridian. The Greenwich
meridian divides the world into the eastern and western hemispheres.
N
15°W
15°E
30°W
30°E
45°W
45°E
60°W
Greenwich (prime) meridian
S
The angle of longitude is the angle a meridian of longitude makes with the Greenwich meridian,
that is, the angle of the ‘wedge’. The diagram illustrates the 35°E meridian of longitude.
O
35°
0°
Angle of Longitude
Meridians of longitude range from 180°W to 180°E. 180°W and 180°E are actually the same
meridian, the line directly opposite the Greenwich meridian on the other side of the Earth.
This is called the International Date Line and runs through the Pacific Ocean east of Fiji. At the
poles, all meridians of longitude meet.
150°W
120°W
150°E
Equator
120°E
The Earth
POSITION COORDINATES
Locations on the Earth are described using latitude (°N or °S) and longitude (°E or °W).
For example, Canberra has coordinates (35°S, 149°E), meaning it is 35° south of the Equator and
149° east of the Greenwich meridian.
Example 1
Match the following coordinates to the points illustrated in the diagram of the Earth.
(a) (50°S, 55°E)
(b) (30°N, 55°E)
(c) (30°N, 0°)
(d) (75°N, 55°E)
(e) (0°, 0°)
(f) (0°, 55°E)
(g) (50°S, 0°)
(h) (75°N, 0°)
Solution
With the Greenwich meridian as illustrated, the meridian of longitude joining Q, S, U and
W is 55°E.
(a) (50°S, 55°E) is point W
(b) (30°N, 55°E) is point S
(c) (30°N, 0°) is point R
(d) (75°N, 55°E) is point Q
(e) (0°, 0°) is point T
(f)
(g) (75°N, 0°) is point P
(h) (0°, 55°E) is point U
(50°S, 0°) is point V
EXERCISE
1. Match the following coordinates to the points illustrated on the diagram of the Earth.
(a) (0°, 100°E)
(b) (40°S, 60°E)
(c) (60°N, 60°E)
(d) (0°, 60°E)
(e) (15°S, 100°E)
(f) (60°N, 100°E)
(g) (15°S, 60°E)
(h) (40°S, 100°E)
2.
Write the coordinates of each of the points illustrated on the diagram of the Earth.
3. Calculate the difference in latitude between these cities, and state whether the second city
listed is north or south of the first.
(a) Shanghai, China (31°N, 121°E) and New York, USA (40°N, 64°W)
(b) Nairobi, Kenya (1°S, 37°E) and Bangkok, Thailand (13°N, 100°E)
(c) Moscow, Russia (55°N, 37°E) and London, UK (51°N, 0°)
(d) Auckland, NZ (37°S, 174°E) and Canberra (35°S, 149°E)
(e) Melbourne (37°S, 145°E) and Cairo, Egypt (30°N, 31°E)
(f) Newcastle (33°S, 151°E) and West Wyalong (34°S, 147°E)
4. Calculate the difference in longitude between these cities, and state whether the second
city listed is east or west of the first.
(a) Budapest, Hungary (47°N, 19°E) and Miami, USA (25°N, 80°W)
(b) Athens, Greece (38°N, 23°E) and Paris, France (49°N, 2°E)
(c) Havana, Cuba (23°N, 82°W) and Mexico City, Mexico (19°N, 99°W)
(d) Buenos Aires, Argentina (34°S, 58°W) and Johannesburg, South Africa
(26°S,28°E)
(e) Manila, Philippines (14°N, 121°E) and Port Moresby, Papua New Guinea
(9°S,147°E)
(f) Finley (35°S, 145°E) and Bourke (30°S, 146°E)
ANGULAR DISTANCE
The angle made at the centre of the Earth by the two points is called their angular distance.
GREAT CIRCLE DISTANCES
Arc length of a circle
In chapter 2 we learned the formula for calculating the length of an arc of a circle.
𝜃
𝑙 = 360 × 2𝜋𝑟 where 𝜃 is the size of the central angle.
𝑟
𝑙
𝜃
𝑟
Example
A shotput circle has a radius of 1.05 m. Calculate the length of the arc AB correct to 3 significant
figures if it makes an angle of 40° at the centre of the circle.
A
40°
B
𝜃
𝑙 = 360 × 2𝜋𝑟
40
= 360 × 2 × 3.142 × 1.05
= 0.733𝑚
Shortest distance between two points on the Earth’s surface
On a flat surface, the shortest distance between two points A and B is a straight line. However, on
the curved surface of a sphere, it is not possible to construct a straight line between A and B.
In this case, the shortest distance between the two points is the arc of the great circle that passes
through those
two points. This can be demonstrated using string on an orange, tennis ball or basketball.
The shortest distance between two points on the Earth’s surface is called the great circle
distance. The angle made at the centre of the Earth by the two points is called their angular
distance. We can use the arc length formula to calculate the shortest distance between the two
points.
A
O
B
Example 5
The diagram shows two points P and Q on the Earth’s surface. The angular distance between
them is 63°.
Calculate the great circle distance between P and Q, to the nearest kilometre, if the radius of the
Earth is 6400 km.
63°
Solution.
𝜃
PQ = 360 × 2𝜋𝑟
63
= 360 × 2 × 3.142 × 6400
= 7037.1675…
= 7037 km
Example 6
Beijing, China and Perth have coordinates (40°N, 116°E) and (32°S, 116°E) respectively.
(a) What great circle joins Beijing and Perth?
(b) What is the angular distance between these two cities?
(c) Hence, calculate the shortest distance between Beijing and Perth, to the nearest kilometre,
given that the Earth’s radius is 6400 km
Solution.
(a) Beijing and Perth both lie on the 116°E meridian of longitude, which is a great circle.
(b) Angular distance = 40° + 32° = 72°
72
(c) Distance = 360 × 2 × 3.142 × 6400
= 8042.4772 …
= 8042km
Small circle distances
Example 7
Moscow, Russia and Copenhagen, Denmark have coordinates (55°N, 38°E) and
(55°N, 12°E) respectively.
(a) What special small circle passes through both cities?
(b) What is the angle between Moscow and Copenhagen at the centre of this small circle?
(c) If the radius of this small circle is 3652 km, use the arc length formula to calculate the small
circle distance between Moscow and Copenhagen, to the nearest kilometre.
55°N
Copenhagen
Moscow
0°
Solution.
(a) Moscow and Copenhagen both lie on the 55°N parallel of latitude, which is a small
circle.
(b) Angle at centre of small circle = 38° − 12° = 26°
26
(c) Small circle distance = 360 × 2 × 3.142 × 6400 × cos 55°
= 1657.2250..
= 1657km
Note: The small circle distance is not the shortest distance between two places.
Global positioning system
A global positioning system (GPS) uses Earth satellites to calculate a person’s location on
Earth. It is possible to purchase a hand-held device that uses GPS technology to calculate your
position coordinates. Investigate how GPS works.
48°N
A
B
0°
D
C
3. (a) What great circle passes through points C and D?
(b) What is the angular distance between C and D?
(c) Calculate the shortest distance between C and D, to the nearest kilometre
(d) What great circle passes through points A and D?
(e) Calculate the great circle distance between A and D, to the nearest kilometre.
(f) What is the distance between points B and C, to the nearest kilometre?
(g) Is the 48°N parallel of latitude a small circle or great circle?
(h) Calculate the distance between A and B, to the nearest kilometre, if the radius of the circle
that goes through them is 4260 km.
THE RADIUS OF A CIRCLE OF LATITUDE
The radius of a (small) circle of latitude can be calculated using trigonometry—in particular,
using the cosine ratio in a right-angled triangle.
In the diagram, the 50°N circle of latitude is shown. Let its radius be r. OR
6367 km is the
radius of the Earth, to the nearest kilometre.
50°N
0°
P
O
𝑟
50°
6367
Equator
T
R
NAUTICAL MILES AND KNOTS
Nautical miles
For sea and air travel, the nautical mile (abbreviated M or nM) is used instead of kilometres.
It has been used for centuries by sailors and navigators because it is directly related to the
latitude–longitude system. A distance of 1 nautical mile (1 M) on the Earth’s surface is
1
equivalent to an angle of 1 minute (60 of a degree) on a great circle of the Earth. Put another
way, 60 nautical miles (60 M) are equivalent to an angle of 1 degree on a great circle.
1′ =
1
°
60
O
We can convert 1 nautical mile to kilometres using the arc length formula,
1
With 𝜃 = 60 ° and 𝑟 = 6367.4 km (a more accurate measure of the Earth’s radius).
𝜃
𝑙=
× 2𝜋𝑟
3601
60
1M = 360
× 2 × 3.142 × 6367.4
= 1.8522…
= 1.852 km.
For many years, Britain and the USA used slightly different values for the size of a nautical mile,
but the international nautical mile has now been defined to be exactly 1.852 km.
1° = 60M on a great circle.
1M= 1.852km
Example 8
(a) The distance between Port Macquarie and Lord Howe Island is 351 M. What is this
distance to the nearest kilometre?
(b) The distance between Hobart and the South Pole is 5280 km. What is this distance to the
nearest nautical mile?
Solution.
(a) Distance between Port Macquarie and Lord Howe Island
= 351 × 1.852
= 650.052
= 650km
(b) Distance between Hobart and the South Pole
= 5280 ÷ 1.852
= 2850.9719
= 2851M
Knots
Nautical and air speed is measured in knots, where 1 knot is 1 nautical mile per hour.
1 knot = 1 nautical mile/hour or 1M/ℎ.
= 1.852 km/ℎ.
Example 9
Between 10 am and 10 pm, a ship sailed 513 M. Calculate its average speed:
(a) in knots
(b) in km/h
Solution.
(a) Time between 10 am and 10 pm = 12 hours
Speed =
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑡𝑖𝑚𝑒
513M
=
12h
= 42.75 knots
(b) Speed = 42.75 × 1.852
= 79.173 km/ℎ.
Example 10
A
C
B
85°
52°N
0°
D
Greenwich
meridian
Calculate:
(a) the distance between points C and D in nautical miles
(b) the distance between points B and D in kilometres
(c) the time it will take a plane to fly from D to B at an average speed of 650 knots
Solution
(a) C and D lie on a great circle, the Equator.
Angular distance = 85°
Distance CD = 85 × 60 M
= 5100 M
(b) B and D lie on a great circle, the 85° E meridian of longitude.
Angular distance = 52°
Distance BD = 52 × 60
= 3120 M
= 3120 × 1.852 km
= 5778.24 km
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
(c) Speed = 𝑡𝑖𝑚𝑒
3120
650 =
𝑡
650𝑡 = 3120
3120
𝑡=
650
= 4.8 hours (or 4 hours 48 minutes)
Note: Using 1° = 60 M and 1 M= 1.852 km to calculate great circle distances is more accurate
𝜃
than using the arc length formula 𝑙 = 360 × 2𝜋𝑟 with 𝑟 = 6400 km, because it involves a more
accurate measurement for the Earth’s radius (6367.4km)
Exercise
Exercise 7-03: Nautical miles and knots
Convert these distances to kilometres.
(a) 750 M (b) 165 M (c) 444 M
2. A yacht sails between two islands in the Pacific Ocean: Norfolk Island (29°S, 168°E) and
Vanuatu (17°S, 168°E).
(a) What is the direction of Vanuatu from Norfolk Island?
(b) Calculate the length of the yacht’s journey in nautical miles.
(c) How long will the journey take if the yacht is sailing at an average speed of 8 knots?
Answer in days and hours.
3. Convert these distances to nautical miles, correct to 1 decimal place.
(a) 100 km (b) 254 km (c) 671 km
4. A plane flies along the 68°S parallel of latitude. How many nautical miles is it from:
(a) the South Pole? (b) the North Pole? (c) the Equator?
5. (a) What is the circumference of the Earth in:
(i) nautical miles? (ii) kilometres?
(b) If a plane travels at an average speed of 440 knots, how long would it take to circle the Earth?
Answer in days and hours
6. Convert these speeds to kilometres per hour.
(a) 77 knots (b) 25 knots (c) 390 knots
7. Calculate the following lengths in nautical miles.
(a) WY
(b) WX
(c) XZ
65°W
75°
0°
Equator
110°W
8. The small circle that runs through points Y and Z in
the diagram in question 7 has a radius of 1648 km.
(a) Calculate the small circle distance between Y and Z using the arc length formula
𝜃
𝑙 = 360 × 2𝜋𝑟 (correct to 2 decimal places).
(b) Convert this distance to nautical miles (correct to 2 decimal places).
If a ship travels 315 nautical miles between 8 am and 6:30 pm in one day, calculate its
average speed:
(a) in knots (b) in km/h
10. Convert 1° on a great circle to kilometres.
11. A plane flew due north from Hobart at a speed of 330 knots for 5 hours.
(a) How far did it travel in nautical miles?
(b) How far did it travel in kilometres?
(c) What is its current position if the coordinates of Hobart are (43°S, 147°E)? Answer
to the nearest degree.
12. Calculate in nautical miles the great circle distances between these cities.
(a) Darwin (12°S, 130°E) and Vladivostok, Russia (43°N, 130°E)
(b) Toronto, Canada (43°N, 79°W) and Panama City, Panama (9°S, 79°W)
(c) Singapore (0°, 103°E) and Quito, Ecuador (0°, 78°W)
(d) Madrid, Spain (40°N, 3°W) and Abidjan, Ivory Coast (5°N, 3°W)
(e) Hanoi, Vietnam (21°N, 106°E) and Ulan Bator, Mongolia (48°N, 106°E)
(f) Mt Isa (20°S, 138°E) and Adelaide (35°S, 138°E)
(g) Bourke (30°S, 146°E) and Townsville (19°S, 146°E)
13. A yacht is sailing due south from Sydney in the Sydney-to-Hobart Yacht Race. What is
its position after travelling 8 hours at a speed of 16 knots if Sydney’s coordinates are
(34°S, 151°E)? Answer to the nearest degree.
14. A cruise ship travels 174 km at an average speed of 28 knots.
(a) Convert 174 km to nautical miles, correct to 2 decimal places.
(b) How long it will take the ship to travel this distance? Answer in hours and minutes.
15. Boston, USA (42°N, 71°W) and Santiago, Chile (33°S, 71°W) are on the same meridian
of longitude.
(a) What is the direction of Boston from Santiago?
(b) Calculate the distance between Boston and Santiago, to the nearest kilometre.
16. An aeroplane is flying south along the Greenwich meridian.
(a) How many nautical miles will it cover after travelling 16° of latitude?
(b) What was its speed in knots if it took 1 hours to cover this distance? Answer
correct to 1 decimal place.
17. The world record for water speed is 250.7 knots, achieved in 1977 at Blowering Lake
Dam, Tumut by Ken Warby in his hydroplane, Spirit of Australia. Calculate, correct to
4 significant figures:
(a) the distance that can be travelled at this speed in 30 seconds, in nautical miles
(b) the same distance in kilometres
(c) 250.7 knots in km/h
18. A ship sailed east along the Equator for 427 nautical miles.
(a) How many whole degrees of longitude were travelled during this time?
(b) How long did this journey take if the ship averaged 14 knots?
Investigation: The antipodes
Two points directly opposite each other on the Earth’s surface are called antipodes
(pronounced ‘an-tip-po-dees’). They are the furthest distance apart that two points on Earth
can be from each other. The Australia–New Zealand region is sometimes nicknamed ‘the
Antipodes’ by the British because we are on the opposite side of the world to them. But are
we exactly?
1. London has coordinates (51°N, 0°). What are the
coordinates of the point X directly on the other side of
the world?
2. Sydney has coordinates (34°S, 151°E). In what direction
is point X from Sydney: NE, NW, SE or SW?
3. What is the difference in latitude and longitude between
Sydney and point X?
4. Find point X in an atlas or on a world globe. What is the
name of the islands that are actually there?
LONGITUDE AND TIME DIFFERENCES
As the Earth spins during the day, the Sun shines on a different part of it. The Earth makes a
complete revolution (360°) every 24 hours.
Spin a world globe (or a basketball with line markings) and use a flashlight to demonstrate
different parts of the world experiencing day and night over a 24-hour period.
When the Sun shines directly on a meridian of longitude, it is 12 noon at all places along that
meridian. The Sun is directly overhead. The word meridian means ‘midday’ in Latin, and
ante meridiem (am) means ‘before midday’ and post meridiem (pm) means ‘after midday’.
When it is midday along a meridian, it is midnight along the opposite meridian (on the other
side of the world).
Since the Earth spins 360° in 24 hours, it will turn 15° in 1 hour. Therefore, there should be
1 hour’s difference in local time per 15° of longitude, or 4 minutes’ difference per 1° of
longitude.
𝟏𝟓° longitude
1 hour’s time difference
𝟏° longitude
4 minutes’ time difference
Around the world, local times are measured relative to the time along the Greenwich meridian
0°, called Greenwich Mean Time (GMT), or Universal Time (UT). Places east of the
Greenwich meridian are ahead of GMT, while places west of the Greenwich meridian are behind
GMT.
Example 12
In New York (east coast USA), the local time is 5 hours behind GMT.
(a) What is the time in New York when the (24-hour) time in London is 1500?
(b) What meridian of longitude passes through New York?
Solution
(a) 1500
5 hours
1000. The local time in New York is 1000 (10 am).
(b) 5 hours’ time difference
5
15°
75° difference in longitude. Since New York is
behind GMT, the meridian of longitude passing through New York is 75°W.
Example 13
In Los Angeles, USA (119°W), a tennis match is played at 2 pm on Tuesday. The
match is televised live to Sydney (151°E). What is the time in Sydney when this match is
played?
Solution.
Difference in longitude = 119° + 151° = 270°
270
Time difference = 15 = 18 hours.
As Sydney is east of GMT and Los Angeles is west of GMT, Sydney time must be ahead of Los
A ngeles time.
Sydney time = 2pm Tuesday + 18 hours = 8 am Wednesday
Example 14
When it is 9 pm in Bombay, India (19°N, 73°E), what is the local time in Jakarta, Indonesia
(6°S, 106°E)?
Solution.
Difference in longitude = 106° − 73° = 33°
33
1
Time difference = 15 = 2 5 hours
= 2h 12min
Or Time difference = 33 ×4minute
= 132 minutes
132
= 60 hours
= 2 hours 12 min
Jakarta is east of Bombay, so its time is ahead of Bombay’s.
Local time in Jakarta
9 pm
2 h 12 min
11:12 pm
The unreality of ‘local time’
In Example 14, the time in Jakarta will not really be 11:12 pm because, as we shall see in the
next part of this chapter, the world is divided into standard time zones. Jakarta is probably in
a time zone where the time is 11:00 pm or 11:30 pm.
However, in the following exercise we shall ignore time zones and calculate ‘local times’
correct to the nearest minute.
Convert these times to 24-hour time.
(a) 6:10 pm (b) 8:46 pm (c) 8:46 am
(d) 3:47 pm (e) 12:30 am (f) 11:15 pm
2. Convert these times to 12-hour (am/pm) time.
(a) 1600 (b) 0530 (c) 2140
(d) 0035 (e) 1905 (f) 1450
3. What is the time:
(a) 7 hours after 7 pm? (b) 10 hours after 9 am?
(c) 8 hours before 2 pm? (d) 6.5 hours before 8 pm?
(e) 2.5 hours after 0300? (f) 15 hours before 0030?
(g) 11 h 18 min after 1315? (h) 7 h 36 min before 1420?
4. The time in Tahiti is 10 hours behind GMT.
(a) What is the longitude of Tahiti?
(b) What is the time in Greenwich (GMT) when it is 6:30 am in Tahiti?
(c) What is the time in Tahiti when it is 6:30 am in Greenwich?
5. Kalgoorlie has coordinates (30°S, 121°E) while the Pacific island of Nauru has
coordinates (0°, 166°E).
(a) Calculate the difference in longitude between the two places.
(b) Calculate the time difference between the two places.
(c) What is the time in Nauru when it is 9:45 am in Kalgoorlie?
6. Hanoi, Vietnam lies on the 105°E meridian while Sydney lies on the 150°E meridian.
When the time in Hanoi is 1730, what is the time in:
(a) Sydney? (b) London (GMT)?
7. The time in Vienna, Austria (48°N, 16°E) is 3 hours before the time in Tehran, Iran.
(a) Calculate the difference in longitude between the two cities.
(b) Hence, what meridian of longitude goes through Tehran?
(c) When it is 2315 in Tehran, what is the time in Vienna? Answer in 12-hour
(am/pm) time.
8. Use the key on your calculator to convert these times to hours and minutes.
(a) 22.7 hours (b) 6.3 hours (c) 4.9 hours
(d) 18.4 hours (e) 10.1 hours (f) 15.6 hours
9. Convert these times to hours and minutes.
(a) 482 minutes (b) 271 minutes (c) 350 minutes
(d) 196 minutes (e) 709 minutes (f) 1214 minutes
(a) Calculate the difference in longitude between New Delhi, India (28°N, 77°E) and
Milan, Italy (41°N, 12°E).
(b) Calculate the time difference between New Delhi and Milan in hours and minutes.
(c) What is the local time in Milan when it is 5 pm in New Delhi?
11. (a) Calculate the time difference between Lisbon, Portugal (38°N, 9°W) and Taipei,
Taiwan (25°N, 121°E).
(b) What is the local time in Taipei when it is 1610 in Lisbon?
12. How many hours and minutes are there from:
(a) 6:30 am to 9:30 pm? (b) 4:30 pm to midnight?
(c) 3 am to 3 pm? (d) 10 am to 5:20 pm?
(e) 8:30 am to 7:46 pm? (f) 4 am to 1:30 am?
13. Early navigators used local times (calculated from the position of the Sun) to determine
their longitude position. Across what meridian of longitude is a ship sailing if its local
time is 6:30 am and GMT shows 11:30 am?
14. An ocean liner’s local time is 5:45 pm when GMT is 8:05 am. What is its longitude
position?
15. Houston, USA has coordinates (29°N, 95°W) while Kabul, Afghanistan has coordinates
(34°N, 70°E). If it is 6:20 pm Sunday in Houston, what is the time in Kabul?
16. Guatemala is 6 hours behind GMT.
(a) What meridian of longitude runs through Guatemala?
(b) What is the time in Britain when it is 1:30 pm in Guatemala?
17. (a) When it is 7:30 pm Monday in Los Angeles, USA (34°N, 119°W), what is the time
in Sydney (34°S, 151°E)?
(b) A plane leaves Los Angeles at 7:30 pm Monday and flies 14 hours to get to
Sydney. What is the local time in Sydney when it arrives?
18. Omsk, Russia and Lord Howe Island, in the Tasman Sea have coordinates (55°N, 73°E)
and (31°S, 159°E) respectively. What is the local time in Omsk when it is 8:30 am on
Lord Howe Island?
19. It is 1430 local time in Alice Springs. What is GMT given that Alice Springs has
longitude 134°E?
20. A ship’s clock shows 1 pm when GMT shows 8 am. What is the longitude position of
the ship?
21. What is the local time in Pretoria, South Africa (25°S, 30°E) when it is 2030 in London,
UK?
22. What is the time in London, UK when the local time in Rio de Janeiro, Brazil
(23°S, 43°W) is 1940?
23. (a) Calculate the time difference between Guangzhou, China (23°N, 113°E) and
Gosford (33°S, 151°E).
(b) If it is midday Saturday in Gosford, what is the local time in Guangzhou?
24. What is the local time in the Falkland Islands, in the South Atlantic (52°S, 60°W) when
it is 8:30 pm Wednesday in Auckland, NZ (37°S, 174°E)?
Study tips
SWITCH OFF THE TV AND THE MOBILE PHONE
It is very easy to achieve nothing in 3 hours of ‘study time’ if much of it is spent on
cleaning your desk, chatting with friends on the phone or Internet, having excessive
fridge and TV breaks, or playing games on the computer. If you are serious about
studying, you need to program into your study routine some blocks of time when
you cannot be interrupted by phone calls or friendly visits. This is
especially important when you have a big task at hand, such as preparing
for an exam or completing a major assignment. Establish an arrangement
with your family so that they know not to disturb you during your study
time.
Get rid of all distractions. Don’t study in front of the TV—time passes
very quickly if you do. Either study or watch TV, but don’t do both. You
can listen to music or have the radio on in your room as long as it doesn’t
affect your concentration. And those fun things you want to do? Do them
during a study break as a reward for completing a significant amount of
work.
Always Learning
@McNotch 2023
Past Year SPM Questions (Paper 1)
1. (2003N, P1, Q15)
In Diagram 8, N is the North Pole, S is the South Pole and NOS is the axis of the earth.
Considering the four points A, B, C and D, which of these is (400 N, 00 E)?
(40°N,60°W) and N are two points on the earth’s surface. If MN is a diameter of the
parallel latitude, the position of point N is
A (40°S,120°W)
B (40°S,120°E)
C (40°N,120°W)
D (40°N,120°E)
3. (November 2004, P1, Q17)
P(150N, 100W), Q and R are three points on the earth surface. Q is due south of P. The
difference in latitude between P and Q is 500. R is due west of Q. The difference in
longitude between Q and R is 700. The position of R is
A (650N, 600E)
B (650N, 800W)
C (350S, 600E)
D (350S, 800W)
23. P(0ºN , 20º E), Q and R are three points on the surface earth. Q is due west of P and R
is the midpoint of PQ The distance between P and R is 3000 nautical miles. Find the
longitude of Q.
A 5 ºE C 5º W
B 70º E D 30º W
24. X( 50º N, 140º E) and Y (60º N, 40º W) are two points on the earth surface. Calculate
the distance in nautical miles between X and Y via North pole.
A 3000 C 4200
B 3600 D 6600
25. P (60 0S, 90 0E) and Q (60 0S, 90 0W) are two points on the surface of the earth.
Calculate the distance in nautical miles from P to Q measured along the common
parallel of latitude.
A 10800 C 5400
B 7200 D 3600
LONGITUDE AND TIME DIFFERENCES
STANDARD TIME We know that places located on different meridians have different local time. It would
create a lot of difficulties, if all countries would adopt different local time.
In Latin a.m. means ante meridian and p.m. means post meridian.
The local time will be ahead at all the places in the east of a given meridian and it will be behind at all
places in the west of a given meridian.